Fig. 4

Equilibrium frequency inference error. Comparison of the accuracy of different methods for reconstructing equilibrium frequencies in the basic simulation scenario (nucleotide characters and tree as in Fig. 1). Violin plots summarise the nucleotide frequency inference error (on the y-axis), measured as the Euclidean distance between the vectors of column-specific simulated nucleotide frequencies and inferred ones. Each plot contains 10 replicates, and each replicate contains 800 alignment columns evolved under the background nucleotide frequencies (a, c and e), or 200 alignment columns evolved under equilibrium nucleotide frequencies sampled from a Dirichlet distribution with \(\alpha =0.1\) (b, d and f). Horizontal black dashed lines aid comparison by showing the median error of the first method (frequencies extracted from character counts). In a and b the tree branch lengths were scaled by a factor of 0.2; in c and d by a factor of 1.0; and in e and f by a factor of 5.0. Each plot shows results for a particular character frequency inference method, indicated on the x-axis. Results from additional methods (e.g. Bayesian approaches) are shown in Additional file 1: Fig. S5